What is the formula for exponential decay?

The formula for exponential decay is $$C(t) = C_0 \times (1 - r)^t$$ , where $$C_0$$ is the initial amount, $$r$$ is the decay rate, and $$t$$ is time.

What does the term 'asymptote' refer to in exponential functions?

An asymptote is a line that a graph approaches but never touches. For exponential decay, the x-axis (y=0) is a horizontal asymptote.

How do you convert an exponential equation to logarithmic form?

To convert $$b^y = x$$ to logarithmic form, use $$y = \text{log}_b(x)$$ .

What is the relationship between exponential functions and logarithms?

Exponential functions and logarithms are inverse functions. The logarithm of a number is the exponent to which the base must be raised to produce that number.

What is the effect of changing the base of an exponential function?

Changing the base affects the rate of growth or decay. A larger base results in faster growth, while a smaller base (greater than 1) results in slower growth.

How do you find the domain and range of an exponential function?

The domain of an exponential function is all real numbers, while the range is all positive real numbers (for growth) or all positive real numbers approaching zero (for decay).

What is a real-world example of exponential growth?

A real-world example of exponential growth is population growth, where the population increases at a rate proportional to its current size.

What is a real-world example of exponential decay?

A real-world example of exponential decay is radioactive decay, where the quantity of a radioactive substance decreases over time at a rate proportional to its current amount.

Alg 2H Unit 6 (Part 1) Review Flashcards

Student preview

15 questions

Show all answers

1.

FLASHCARD QUESTION

Front

What is an exponential function?

Back

2.

FLASHCARD QUESTION

Front

What does the base of an exponential function represent?

Back

3.

FLASHCARD QUESTION

Front

How do you identify an exponential growth function from a graph?

Back

4.

FLASHCARD QUESTION

Front

What is the general form of an exponential decay function?

Back

5.

FLASHCARD QUESTION

Front

What is the significance of the y-intercept in an exponential function?

Back

6.

FLASHCARD QUESTION

Front

How can you determine the equation of an exponential function from a graph?

Back

To determine the equation, identify the y-intercept and the base by observing the growth or decay rate of the graph.

7.

FLASHCARD QUESTION

Front

What is the formula for exponential growth?

Back

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